7. LS-DYNA Anwenderforum, Bamberg 2008

Numerical Modelling of Cross Roll Straightening

A. Mutrux, B. Berisha, B. Hochholdinger, P. HoraInstitute of Virtual Manufacturing, ETH Zurich

CLA F19.3, Tannenstr.3, 8092 Zurich, Switzerlandmutrux@ivp.mavt.ethz.ch

Summary:The aim of the cross-roll straightening process is to straighten bars having a circular section. To the knowl-edge of the authors, most of the work published about this process is based on analytical considerations.In the present study, the process is explained and simulatedusing LS-Dyna. The similarity between threepoints bending and cross-roll straightening is highlighted. In order to test the straightening ability of thesimulation, a bent bar is used as an input for the simulation.Comparing the curvatures of the in- andoutput bars, it appears that a reduction of the curvature canbe predicted.

Keywords:cross roll straigthening, straightness prediction.

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1 The cross roll straightening process

1.1 Straightening machines

Metal products – such as bars, rails, and sheets – can be straightened by alternate bending with a decreas-ing amplitude. Ideally, the last bending step produces sucha curvature that, after springback, the productreaches straightness (or flatness). For example, railway rails are straightened by passing through sets ofalternate rolls, as depicted in figure (1), where they are reversely bent in one plane.

Figure 1: Schematic straightening of railway rails (from [1]).

For bars, the problem is slightly different. Whereas rails tend to bend in one plane due to the differentmoments of inertia of their section, round bars can bend freely in three dimensions. One solution allowingto straighten such products in space is to bend the material in two planes normal to each other by settingtwo devices as depicted in figure (1) at a right angle. A characteristic of bars is their ability to be rotatedeasily around their main axis, even under stress. Based on this fact, another option is to bend the productand make it rotate simultaneously. This second possibilityresults in processes such as shown in figure (2).

Figure 2: Bar straightening in a cross roll straightening machine (from [2]).

1.2 Deformation path

Figure (2) shows the principle of cross roll straightening –that is the process studied in this paper. Thebar passes through two rolls: a concave one and a convex one. As long as the distance between the rollsis larger than the diameter of the bar, the bar undergoes purebending. For rods having a large diameter,the rolls may also stamp the material – this case is not studied in this paper. Considering a point on thesurface of the bar, its path in space is along a helix with a bent axis. As pictured in figure (3), the resultingstrain state can be represented as one of a three points bending progressing along a helix. The bending of

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Figure 3: The plastic zone in the bent rod is propagatedalong a helix (from [5], modified).

Figure 4: The angleα between the rollsand the bar.

the bar can be controlled by varying the angleα between the rolls and the bar (see figure (4)): the smallertheα, the more bending occures. The optimalα is such that the highest straightness of the bar is reachedwhile still having an economically realistic translation speed. Nowadays, the choice ofα is made mostlyon an empirical basis.

Analytical approaches of the straightening process can be found in the references (particularly [4] and[6]). Nevertheless, these approaches are based on numerousmore or less offhand hypotheses. To theknowledge of the authors, most of the research done about cross roll straightening was done during thepre-simulative era. A deeper understanding of the process is expected through the use of LS-Dyna.

1.3 Bending simulation

As mentionned above, cross roll straightening is a repetitive bending process. Before simulating the wholecross roll straightening process – with the rotating rolls –a simulation is made where the rod is simplybent by the closing of the rolls. Figure (5) shows the stress distribution of the upper elements (in contactwith the concave roll) of the bar during bending as a functionof their position along the bar axis. Thesimulation parameters are the same as for the cross rolling simulation described below. Only the elementsin the middle of the bar reach plastic deformation. As it willbe shown later, the stress distribution obtainedcorresponds to the stress envelope of an element passing through the rolls in the full cross roll simulation.

2 The simulation of the cross roll straightening process

2.1 Geometry

In figure (6), one can see the different parts of the model. Therod itself – meshed with fully integrated(type 2) volume elements – is number 1. Part 2 is modelled withbeams and represents the extension of therod. These beam elements are never in contact with the rolls:their sole purpose is to give the rod a realistic

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Figure 5: Axial stress of the elements in contact with the concave roll during the closing of the rolls(simple three points bending simulation) as a function of their position along the bar axis.

Figure 6: The different parts of the model. The rod (part No 1)moves from right to left as the rolls (partsNo 3 and 4) rotate.

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behaviour during both the gravity and the rolling operations by remaining in the box defined by parts 6aand 6b. The beams are fixed to the rest of the bar using a *CONSTRAINED NODAL RIGID BODY. Parts3 and 4 are, respectively, the convex and concave rolls: bothmeshed with shell elements and consideredas rigid bodies. The guides 5a and 5b, also rigid bodies, keepthe rod in place during the whole simulation.

2.2 Process

The simulation is divided in three main steps:

1. gravity: the rod falls on the convex roll due to gravity.

2. closing: the rolls close and bend the bar.

3. rolling: the rolls rotate – this operation is the ’core’ of the process.

The rod considered in the simulation is 10 [m] long: 1.5 [m] ismeshed with volume elements and the restis discretised with beams. This avoids, using a technique quite close to reality, extra constraints to appearin the rod due to the oscillation of the bar. The main drawbackof this method is that thegravity operationhas to be long enough before the bar stops swinging in the box.To reduce computation time, a mixed timeintegration strategy is chosen: thegravity is computed with the ’implicit’ flag turned on and the rest ofthe simulation is integrated explicitly.

After the gravity step, theclosing of the rolls takes place, during which the concave roll is translatedtowards the convex one, bending the bar. Once, the bar is bent, the properrolling takes place. Duringrolling, the only loads applied are the ones induced by the rigid bodyrotations of the rolls. The contactbetween the rolls and the rod is done with theSMOOTH option turned on, thus allowing to use a reducednumber of elements to model the rolls.

2.3 Material behaviour

Compression-tension tests have been done on the material tobe straightened – the results can be seenin figure (7). One observes a different yield stress for the second part of the deformation (the tensiledeformation). This difference in yield stress can be explained by the kinematic hardening behaviourof the material. In cross-roll straightening, the materialalso undergoes reverse loading – an isotropicmaterial model would necessarly be a major simplification. For the present simulation, a purely kinematichardening model is fitted to the experimental data (*MATPLASTIC KINEMATIC). Future work shallinclude a more complex kinematic behaviour, such as the model proposed by Chaboche [10].

Figure 7: Different plastic pre-straining in compression with a subsequent tension loading

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2.4 Simulation results

The stress state obtained is uniaxial – radial stresses do not exceed 10 [Mpa]. The general shape of the ax-ial stress on one element (see figure (8)) corresponds to whatone would have expected after seeing figure(5). From the theoretical pitch of the helix mentionned above: p = 2πr tan(α) ≈ 24 [mm] (for r = 12.5[mm] andα = 17 [deg]) and knowing that the distance between the three contact points in the simulationis about 480 [mm], the number of peaks should be 480/24 = 20. As can be seen in figure (8), there areabout 10 peaks in the first part of the straightening itself.

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Figure 8: Axial stress acting on an element on the outer layerof the rod as a function of its positionbetween the rolls. The stress envelope corresponds to the stress distribution obtained in bending.

Concerning the smaller stress peaks outside the envelope, apossible explanation is the swinging of therod when it is not in the rolls. The stress envelope plotted infigure (8) is only a translation in X of theresults plotted in figure (5). The good agreement between thestress peaks from the rolling simulationand the stress distribution from the bending simulation prove the validity of the assumption mentionnedearlier: the reduction of the cross rolling simulation to a series of alternate bendings. In the second part ofthe graph (after the maximum stress peak), one can observe a discrepancy between the two curves. Thisphenomenon may be explained by the fact that, in the bending simulation, the elements on the right handside have no deformation history – they have not been bent back and forth. In order to account preciselyfor a kinematic hardening behaviour of the material, the whole process has to be simulated.

3 The straigthening effect prediction

In order to test the straightening ability of the model, a curved bar with a radius of curvature (in a singleplane) about 9400 [mm] is used as an input. The definition of straightness is normally related to an axiallength, typically the maximum deviation from a perfect lineon 1 [m]. Applying such a criterion to thepresent problem would require simulating the process with very long bars, which would lead to excessivecomputation times. To circumvent this problem, the straightness of the product is defined through itscurvature in the middle of a 100 [mm] rod segment. Nodes on themiddle axis of the rod are taken asreferences and a plane is fitted across them. On the fitted plane, a two-dimensional coordinate system isbuilt, from which a parabola is fitted through the points. Thesecond derivative of the parabola correspondsto the local curvature of the rod. The adequate number of points to be taken for the fit is a delicate issue.

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If too few points are taken, numerical errors gain greater importance. But, as the output rod has generallya three dimensional curvature, the more nodes are taken, thefarther they are from the fitted plane, whichalso induces errors. Therefore, the number of nodes to be taken depends on the curvature with which onehas to deal: a few trials are recommended.

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Figure 9: Parabola fitted to in- and output nodes from the median line of the rod in the XY plane.

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Figure 10: In- and output rod curvatures in the XZ plane.

Figures (9) and (10) show the rod curvature before and after the straightening process. As it can be seen,whereas the input rod is only curved in one plane, the curvature of the output rod is three-dimensional. Inthe example taken, the radius of curvature of the bar after straightening is about 100·103 [mm].

4 Summary

Based both on workshop observations and on the references below, a cross-roll straightening device hasbeen simulated. The similitude between the stress state obtained in three points bending and in cross-rollstraightening has been highlighted. By passing through therolls, the curvature of a bent bar can be signif-icantly reduced.

The kinematic hardening behaviour of the material is to be more precisely investigated. In the simulationpresented here, a simple linear hardening kinematic is used. Future work shall consider more complexhardening models.

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References

[1] Srimani, S.L. and Basu, J. An investigation for control of residual stress in roller-straightened rails,J. Strain Analysis, Vol. 38, No.3 , 2003, 261–268

[2] Das Talukder, N.K. and Johnson, W. On the arrangement of rolls in cross-roll straighteners,Int. J.Mech. Sci., Vol. 23, 1981, 213–220

[3] Das Talukder, N.K and Singh, A.N. Mechanics of bar straightening, Part 1: general analysis ofstraightening process,Trans. A.S.M.E, Vol. 113, 1991, 224–227

[4] Das Talukder, N.K and Singh, A.N. Mechanics of bar straightening, Part 2: straightening in cross-rollstraighteners,Trans. A.S.M.E, Vol. 113, 1991, 228–232

[5] Fangmeier, R. Untersuchungen uber das Richten von Rundstaben in zwei-Walzen-Richtmaschninen,Doctoral Thesis, Technischen Hochschule Claustahl, 1966

[6] Yu, T.X. and Johnson, W. Estimating the curvature of barsafter cross roll straightening,Proc. 22ndInt. Machine Tool Des. and Res. Conf. (MTDR), Manchester, UK, 1981, 517–521

[7] Yu, T.X. and Zhang, L.C. Plastic bending: theory and applications, World Scientific Publishing,USA, 1996

[8] Wu, B.J. and Chan, L.C. A study on the precision modeling of the bars produced in two cross-rollstraightening,J. Materials Processing Technology, 2000, 202–206

[9] Schleinzer, G. and Fischer, F.D. Residual stresses in new rails,J. Materials Science and Engineering,2000, 280–283

[10] Chaboche, J.L. Constitutive equations for cyclic plasticity and cyclic viscoplasticity,Int. J. Plasticity,Vol. 5, 1989, 247–302

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